Re: WND Files Suit Against White House Press Corps

In answer to my own question, it appears that it is a private organization (composed of journalists covering the White House) which has been granted a monopoly (on access to the President) by the government.

Interesting quote in the wikipedia page:

Originally Posted by wikipedia

After the 2007 dinner, New York Times columnist Frank Rich implied that the Times will no longer participate in the dinners.[4] Rich said that the event is "a crystallization of the press's failures in the post-9/11 era" because it "illustrates how easily a propaganda-driven White House can enlist the Washington news media in its shows."[4]